Coefficient of Partial Correlation and Its Calculation

This thesis offers the general concept of coefficient of partial correlation.Starting with regres-sion analysis,the paper,by using samples,infers the general formula of expressing coefficient of partial correlation by way of simple correlation coefficient.

Zonal Differences in Correlation Patterns Between Soil Organic Carbon and Climate Factors at Multi-extent

Studying the relationship between climate factors and soil organic carbon （SOC） is vitally important. However, how SOC responses to climate （temperature and precipitation） at cohesive extents is poorly studied. Two transects of approximately the same length （transect P and transect T） were selected to examine the variation of SOC content in relation to mean annual temperature （MAT） and mean annual precipitation （MAP）. The coefficients of partial correlation between SOC density and MAT （Rt） and MAP （Rp） were determined to quantify the relationships between SOC density and the two climate factors. The results indicated that for transect T, Rt was statistically significant once the extent level was greater than or equal to two fundamental extent units, while for transect P, Rp showed statistical significance only at extent levels which were greater than two fundamental extent traits. At the same extent levels but in different transects, Rts exhibited no zonal difference, but Rps did once the extent level was greater than two fundamental extent units. Therefore, to study the relationship between SOC density and different climate factors, different minimum extent levels should be ex- amined. The results of this paper could deepen the understanding of the impacts that SOC pool has on terrestrial ecosystem and global carbon cycling.

AR Model Based on Time Series Modeling for Predicting Egg Market Price in 2021

Eggs,as a meat consumer product in China,are closely related to the vegetable basket project.Exploring and predicting the future trend of egg market price is of great significance for stabilizing egg price and market supply.In this study,the time series AR model was used for fitting the egg market prices in the 66 d from January 1 to March 7,2021,and the delay operator nlag18 was used for white noise test,giving pr>probability of chisq<0.005.The time series was not a white noise series,and then the stationary series was used for modeling.The optimal model was selected as the AR series(BIC(3,0)),and finally,the egg market price model AM was obtained as X_(t)=9.0556+(1+0.8926)ε_(t),which was the optimal model.The model showed that the egg price fluctuations in 2021 will be clustered,and the later price will be significantly affected by external factors in the previous period.The dynamic prediction results of the model showed that the egg price would stop falling in March 2020,and the egg price would continue to slow down in March.

Parameter Sensitivity and Qualitative Analysis of Dynamics of Ovarian Tumor Growth Model with Treatment Strategy

In this paper, we are interested to find the most sensitive parameter, local and global stability of ovarian tumor growth model. For sensitivity analysis, we use Latin Hypercube Sampling (LHS) method to generate sample points and Partial Rank Correlation Coefficient (PRCC) method, uses those sample points to find out which parameters are important for the model. Based on our findings, we suggest some treatment strategies. We investigate the sensitivity of the parameters for tumor volume, y, cell nutrient density, Q and maximum tumor size, ymax. We also use Scatter Plot method using LHS samples to show the consistency of the results obtained by using PRCC. Moreover, we discuss the qualitative analysis of ovarian tumor growth model investigating the local and global stability.

Energy consumption hierarchical analysis based on interpretative structural model for ethylene production

Interpretative structural model(ISM) can transform a multivariate problem into several sub-variable problems to analyze a complex industrial structure in a more efficient way by building a multi-level hierarchical structure model. To build an ISM of a production system, the partial correlation coefficient method is proposed to obtain the adjacency matrix, which can be transformed to ISM. According to estimation of correlation coefficient, the result can give actual variable correlations and eliminate effects of intermediate variables. Furthermore, this paper proposes an effective approach using ISM to analyze the main factors and basic mechanisms that affect the energy consumption in an ethylene production system. The case study shows that the proposed energy consumption analysis method is valid and efficient in improvement of energy efficiency in ethylene production.

Global sensitivity analysis of a single-cell HBV model for viral dynamics in the liver

The predictive accuracy of mathematical models representing anything ranging from the meteorological to the biological system profoundly depends on the quality of model parameters derived from experimental data.Hence,robust sensitivity analysis(SA)of these critical model parameters aids in sifting the influential from the negligible out of typically vast parameter regimes,thus illuminating key components of the system under study.We here move beyond traditional local sensitivity analysis to the adoption of global SA techniques.Partial rank correlation coefficient(PRCC)based on Latin hypercube sampling is compared with the variance-based Sobol method.We selected for this SA investigation an infection model for the hepatitis-B virus(HBV)that describes infection dynamics and clearance of HBV in the liver[Murray&Goyal,2015].The model tracks viral particles such as the tenacious and nearly ineradicable covalently closed circular DNA(cccDNA)embedded in infected nuclei and an HBV protein known as p36.Our application of these SA methods to the HBV model illuminates,especially over time,the quantitative relationships between cccDNA synthesis rate and p36 synthesis and export.Our results reinforce previous observations that the viral protein,p36,is by far the most influential factor for cccDNA replication.Moreover,both methods are capable of finding crucial parameters of the model.Though the Sobol method is independent of model structure(e.g.,linearity and monotonicity)and well suited for SA,our results ensure that LHS-PRCC suffices for SA of a non-linear model if it is monotonic.